Well I wasn't aware of the New Yorkshire thing until I looked it up, but I know a fair bit about colonial governance in British America due to research I did for LTTW. In colonial times the Province of New York was governed from New York City by the Governor (or more usually Lieutenant-Governor, many Governors being absentee), the New York Assembly and the Executive Council. I'm not sure if they had a permanent meeting place, although there seem to be a fair few references to them meeting in Fort Amsterdam (AKA Fort James and a host of other names). It was demolished in 1790 after the American Revolution, which may be why it's not well known.
Thande, I have a long-planned timeline in the works dealing with the same time period. Are there any good resources you can recommend on the issues that came up in your timeline?